TR-2004-11

Rigid realizations of graphs on small grids

Abstract

A framework (G,p) is a graph
G=(V,E) and a mapping
p: V \to R2. We prove that if
(G,p) is an infinitesimally rigid framework
then there is an infinitesimally rigid framework (G,q)
for which the points q(v), v \in V(G), are distinct points of
the k * k grid, where k=\lceil {\sqrt{|V|-1}}\rceil+9.
We also show that such a framework on G can be constructed
in O(|V|3) time.